Another important aspect of Dedekind's views about functions is that, with respect to the intended range of functions, he allows for arbitrary injective correlations between sets of numbers, indeed between sets of objects in general.

To give but the simplest example, Riemann was an enthusiastic follower of Dirichlet's idea that a function has to be conceived as an arbitrary injective correspondence between numerical values, be it representable by a formula or not; this meant leaving behind the times when a function was defined to be an analytic expression.

The four companies include one that produces innovative plastic-injective molding, one is wood related, another is involved in high-tech assembly and another is aviation related, Heird told board members.